{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:08Z","timestamp":1753893848873,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The distinguishing chromatic number, $\\chi_D(G)$, of a graph $G$ is the smallest number of colors in a proper coloring, $\\varphi$, of $G$, such that the only automorphism of $G$ that preserves all colors of $\\varphi$ is the identity map. \u00a0Collins and Trenk conjectured that if $G$ is connected with girth at least 5 and $G\\ne C_6$, then $\\chi_D(G)\\leqslant \\Delta+1$. We prove this conjecture.<\/jats:p>","DOI":"10.37236\/7170","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:20:16Z","timestamp":1578669616000},"source":"Crossref","is-referenced-by-count":2,"title":["Proper Distinguishing Colorings with Few Colors for Graphs with Girth at Least 5"],"prefix":"10.37236","volume":"25","author":[{"given":"Daniel W.","family":"Cranston","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,7,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:30:44Z","timestamp":1579235444000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i3p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,13]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/7170","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,7,13]]},"article-number":"P3.5"}}